Pith Number

pith:XZTVGEQF

pith:2024:XZTVGEQFE2VGOCQY4MQVGISSHT

not attested not anchored not stored refs pending

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity

Marcelina Mocanu

arxiv:2412.20560 v1 · 2024-12-29 · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZTVGEQFE2VGOCQY4MQVGISSHT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T09:55:19.014565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be6753120526aa670a18e3215322523ce4488a9eec217f3e1f44379cec89cef9

Aliases

arxiv: 2412.20560 · arxiv_version: 2412.20560v1 · doi: 10.48550/arxiv.2412.20560 · pith_short_12: XZTVGEQFE2VG · pith_short_16: XZTVGEQFE2VGOCQY · pith_short_8: XZTVGEQF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: be6753120526aa670a18e3215322523ce4488a9eec217f3e1f44379cec89cef9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35c0a36d2229d1b3edf3df3019087478ff29718bd73d1635aa5d08a2caa0d324",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2024-12-29T19:53:34Z",
    "title_canon_sha256": "3c6e42d1ac82937aa53b754010e4e1c9729ec2c2404b908f71d4749adc3178ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.20560",
    "kind": "arxiv",
    "version": 1
  }
}